Anisotropic Landau-Lifshitz sigma models from q-deformed AdS_5 x S^5 superstrings

Abstract

We consider bosonic subsectors of the q-deformed AdS_5 x S^5 superstring action and study the classical integrable structure of anisotropic Landau-Lifshitz sigma models (LLSMs) derived by taking fast-moving limits. The subsectors are 1) deformed AdS_3 x S^1 and 2) R x deformed S^3. The cases 1) and 2) lead to a time-like warped SL(2) LLSM and a squashed S^3 LLSM, respectively. For each of them, we construct an infinite number of non-local conserved charges and show a quantum affine algebra at the classical level. Furthermore, a pp-wave like limit is applied for the case 1). The resulting system is a null-like warped SL(2) LLSM and exhibits a couple of Yangians through non-local gauge transformations associated with Jordanian twists.

38 pages, 1 figure, typos corrected, minor comments and references added

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• Field theory generalizations of two-body Calogero-Moser models in the form of Landau-Lifshitz equations
• Three-parameter deformation of $\mathbb{R}\times S^3$ in the Landau-Lifshitz limit
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• An integrable deformed Landau-Lifshitz model with particle production?